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Chapter 28: Problem 32

Resonance is a phenomenon which occurs in RLC circuit, during which impedance due to capacitor and inductor become equal and peak current is achieved in the circuit. At resonance the impedance of the circuit is lowest and equal to the resistance in the circuit The value of peak current / is given as follows: \(I=\frac{V}{r}\) Here, \(V\) is voltage in RLC circuit and \(r\) is resistance in the circuit.

Short Answer

Expert verified
The peak current in the RLC circuit when resonance is achieved can be calculated by using the formula \(I = V/r\). Substitute the given values of voltage and resistance into this equation to determine the peak current.

Step by step solution

01

Identify the Variables

In the given equation, \(I\) represents the peak current, \(V\) is the voltage in the RLC circuit, and \(r\) is the resistance in the circuit.
02

Substitute the Values Into the Equation

Replace \(I\), \(V\), and \(r\) in the equation \(I = V/r\) with the corresponding values from the problem statement.
03

Calculate the Peak Current

Perform the division \(V/r\) to find the peak current, \(I\). That value you obtain will be your answer for the peak current.

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Most popular questions from this chapter

The FM radio band covers the frequency range \(88-108\) MHz. If the variable capacitor in an FM receiver ranges from \(10.9 \mathrm{pF}\) to \(16.4 \mathrm{pF},\) what inductor should be used to make an \(L C\) circuit whose resonant frequency spans the FM band?

A series \(R L C\) circuit with \(R=1.3 \Omega, L=27 \mathrm{mH},\) and \(C=\) \(0.33 \mu \mathrm{F}\) is connected across a sine-wave generator. If the capacitor's peak voltage rating is \(600 \mathrm{V},\) what's the maximum safe value for the generator's peak output voltage when it's tuned to resonance?

A \(470-\Omega\) resistor, \(10-\mu \mathrm{F}\) capacitor, and \(750-\mathrm{mH}\) inductor are each connected across \(6.3-\mathrm{V}\) rms, \(60-\mathrm{Hz}\) AC power. Find the rms current in each.

Your professor tells you about the days before digital computers when engineers used electric circuits to model mechanical systems. Suppose a \(5.0-\mathrm{kg}\) mass is connected to a spring with \(k=1.44 \mathrm{kN} / \mathrm{m} .\) This is then modeled by an \(L C\) circuit with \(L=2.5 \mathrm{H} .\) What should \(C\) be in order for the \(L C\) circuit to have the same resonant frequency as the mass-spring system?

An electric drill draws \(4.6 \mathrm{A}\) rms at \(120 \mathrm{V}\) rms. If the current lags the voltage by \(25^{\circ},\) what's the drill's power consumption?
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